G1 Range Restricted Data Interpolation Using Bézier Triangular Patch
Loading...
Date
2015-02
Authors
PING, SI
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The construction of range restricted G1 parametric surface to data that all lie on one
side of a constraint plane is considered. The interpolating surface is developed
piecewise as the convex combination of three quartic Bézier triangular patches.
Sufficient tangent plane continuity conditions along the common boundary of two
adjacent quartic Bézier triangular patches are presented. Sufficient range restriction
conditions are derived which imposed the lower bound to Bézier points. In addition,
supplementary conditions to ensure the range restriction of two adjoining triangular
Bézier patches are presented. The normal vectors are estimated at the data sites by a
local estimation method. The Bézier points are initially determined by the data points
and the estimated normal vectors at data, and such that the interpolant is G1
continuous across one of the triangle boundaries. The Bézier points are then modified
if necessary so that the sufficient range restriction condition is fulfilled in
conjunction with the continuity condition. The resulting surface is G1 continuous
and lies on the same side of the constraint plane as the given data. Some examples
are presented graphically.
Description
Keywords
G1 Range Restricted Data Interpolation , Using Bézier Triangular Patch